Implementing a Function Using Look-Up Tables

[Vishera]

Homework Statement

Homework Equations

The Attempt at a Solution

I am unsure how to proceed from here. Here is what I understand LUTs to look like:

Here is my attempt so far:
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[Vishera]

Do LUTs need to look exactly like this below? Or can LUTs be any sort of box that has 2 inputs and 1 output?

Also, do LUTs need those pink squares? i.e. stored 1's and 0's inside the LUT as memory.